Reduced-Bias Location-Invariant Extreme Value Index Estimation: A Simulation Study

MEAN-OF-ORDER-p LOCATION-INVARIANT EXTREME VALUE INDEX ESTIMATION

• A simple generalisation of the classical Hill estimator of a positive extreme value index (EVI) has been recently introduced in the literature. Indeed, the Hill estimator can be regarded as the logarithm of the mean of order p = 0 of a certain set of statistics. Instead of such a geometric mean, we can more generally consider the mean of order p (MOP) of those statistics, with p real, and eve...

Improving Second Order Reduced Bias Extreme Value Index Estimation

• Classical extreme value index estimators are known to be quite sensitive to the number k of top order statistics used in the estimation. The recently developed second order reduced-bias estimators show much less sensitivity to changes in k. Here, we are interested in the improvement of the performance of reduced-bias extreme value index estimators based on an exponential second order regressi...

A location-invariant probability weighted moment estimation of the Extreme Value Index

On Maximum Likelihood Estimation of the Extreme Value Index

Received November 2002; revised June 2003. Supported by Netherlands Organization for Scientific Research through the Netherlands Mathematical Research Foundation and by the Heisenberg program of the DFG. Supported in part by POCTI/FCT/FEDER. AMS 2000 subject classifications. Primary 62G32; secondary 62G20.

Comparison at Optimal Levels of Classical Tail Index Estimators: a Challenge for Reduced-bias Estimation?∗

In this article, we begin with an asymptotic comparison at optimal levels of the so-called “maximum likelihood” (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same ...